Do Researchers and Rule of law go together across countries?

Across 131 countries the link before adjusting for anything is r = +0.79, on a scale from -1 (opposite) to +1 (in step). A version that uses only each country's rank gives +0.75.

Does the link hold within countries over time, not just across countries?

Comparing each country only with itself across 1996-2024, and setting aside what happened worldwide in each year, the link is +0.028 (101 countries, 1,721 country-years). Using year-to-year changes, it is +0.008.

Does Researchers cause Rule of law?

This analysis cannot answer that. It shows only that the two go together. A link between two country measures, adjusted or not, does not show that either one changes the other. Country figures also say nothing about individual people.

Researchers vs. Rule of law

Holds up after adjusting for income

Across 131 countries, Researchers and Rule of law rise and fall together at r = +0.79 (on a scale from −1 to +1, where 0 means no link). Comparing only countries with similar income (GDP per person) shrinks it to +0.56 (q = 0.016, allowing for the many pairs tested). Much of the first figure is that both measures rise with national income, but a moderate positive link remains.

Comparing countries across the middle half of researchers, 139 to 3,181 per million people, rule of law is better by 0.934 points at the top of that range than the bottom. Comparing only countries with similar national income, the gap is 0.597 points.

Link before adjusting (r)+0.786p = 9.9e-29 · 131 countries

After adjusting for national income+0.561p = 3.7e-12 · likely range [+0.43, +0.67]

p, allowing for regions0.001standard error 0.086 · 7 regions

Check for luck (q)0.016across 12,497 pairs

How to read these.r runs from −1 (one goes up as the other goes down) to +1 (they rise together), and 0 means no link. Adjusting for national income means comparing countries with the same GDP per person, so differences in wealth can’t explain the link. Income is used in percentage terms, since an extra $1,000 means more to a poor country than to a rich one. p is how likely a link this strong would be if there were really none. Below 0.05 means it is unlikely to be chance. Very small values are written in short form: 1.1e-32 means a decimal point followed by 31 zeros and then 11, so very close to zero. The likely range is where the true figure probably lies, and a range that crosses zero means the link could easily be chance. Countries in the same region tend to resemble each other, so the third figure allows for that, which gives a fairer p. The standard error is the typical size of the error in r. Finally, testing this many pairs means some will look strong by luck alone. A q below 0.05 means this link is unlikely to be one of those.

Researchers · per million peoplelink with income +0.85 · proxy

Rule of law · index (approx. -2.5 to 2.5)link with income +0.72 · high

Both of these rise and fall closely with national income, so a strong link between them before adjusting was close to certain. Read the adjusted figure, not the first one.

“Link with income” is how closely each measure tracks GDP per person across countries, from −1 to +1.

Every country as a dot

best-fit line line after adjusting

Four ways to measure the link

Method	r	p	Countries
Standard (Pearson), not adjusted	+0.786	9.9e-29	131
By rank (Spearman), not adjusted	+0.749	7.8e-25	131
Standard (Pearson), adjusted for national income	+0.561	3.7e-12	131
By rank (Spearman), adjusted for national income	+0.208	0.017	131

The rank version uses only each country’s place in line, from lowest to highest, so a few extreme countries count for less. The adjusted and unadjusted versions use the same 131 countries: those that report both measures and GDP per person. So the gap between them comes from the adjustment, not from a change in which countries are counted. Drop in the size of r after adjusting: +0.225 (a minus sign means it grew).

How solid is it?

Leaving out one country at a time, r ranges from +0.542 (without FIN) to +0.576 (without BTN). The bar above shows that range on a scale from −1 to +1, with the solid line at the full result. The single country that moves r most: FIN (-0.019).

Within each region

Countries are not separate, unrelated cases, and neighbors share a lot. A link that holds inside each region is far more believable than one that shows up only when comparing regions.

	n	r
East Asia & Pacific	18	+0.45
Europe & Central Asia	45	+0.56
Latin America & Caribbean	17	+0.21
Middle East, North Africa, Afghanistan & Pakistan	17	-0.00
Sub-Saharan Africa	29	+0.32

By income third

If the link shows up only in the richest third of countries, it is a feature of rich countries, not a general pattern.

	n	r
Poorest third	44	+0.21
Middle third	43	-0.17
Richest third	44	+0.71

By largest religious group

Countries grouped by a label they share, such as main religion, rather than by a number. Groups of fewer than twelve countries are not shown. These groups differ in income, region and history all at once. So a gap between them is a place to start asking questions, not an answer.

	n	r
Christians	80	+0.64
Muslims	32	-0.27

By last european coloniser

	n	r
France	13	+0.40
Never a European colony	15	+0.48
Spain	16	+0.43
United Kingdom	36	+0.47

Without outliers (countries far outside the middle half of countries on either measure, by more than one and a half times the width of that middle half): r = +0.529 after dropping 5 countries.

Two series, one country

Both measures over the years for one country you pick. The two charts are stacked so they share only the years along the bottom.

Loading…

Over time, within countries

Everything above compares countries with each other at one moment. This section compares each country only with itself over 29years. So a link here can’t come from anything about a country that stays the same, such as its history, geography, institutions or culture.

Within countries over time, there is no link that is clearly more than chance (r = +0.028, comparing each country only with itself over the years, and each year only with the same year elsewhere). Whatever the cross-country picture shows, countries whose researchers moved did not tend to see their rule of law move with it.

Across countries (adjusted)+0.561for comparison

Within countries-0.001each country vs itself

…and vs the same year elsewhere+0.028q = 0.829 · 101 countries

Year-on-year changes+0.008q = 0.877

Read with care.

Almost all of the second indicator's variation is between countries, so the within-country estimate rests on a small part of the data.

1,721 country-years (one country in one year), 101 countries, 1996–2024, about 17 years each on average. Share of the variation that happens within countries over time: 12% for Researchers, 3% for Rule of law. The margins of error allow for each country appearing many times, and for each year’s value being close to the year before.

Year-to-year changes are a cautious test, not a final answer. Looking only at changes from one year to the next removes each country’s own trends. But it also makes measurement mistakes louder, which pulls the results toward zero. A near-zero result here is weak evidence of no link, not proof.

With one measure years behind the other

Same year (lag 0): +0.028. A peak away from zero does not show which comes first. These series change slowly — this year’s value is close to last year’s. That makes the curve smooth and nearly symmetric, whatever produced the data. Even a sharp peak at one lag (a gap of some years) would not prove that one measure changes the other.

The largest value on this curve (+0.08 at lag -6) is higher than the same-year one by 0.05. That gap is not a finding. It is the largest of 21 closely related estimates, and picking the biggest of many tests always makes it look bigger. That is exactly why nothing on this site is ranked or chosen by lag.

The data

	per million people	index (approx. -2.5 to 2.5)	Years
Korea, Rep. KOR	9,472	1.12	2023, 2024
Sweden SWE	8,911	1.73	2023, 2024
Denmark DNK	8,838	2	2023, 2024
Singapore SGP	8,782	1.43	2022, 2024
Finland FIN	8,315	2.02	2023, 2024
Norway NOR	7,451	1.95	2023, 2024
Austria AUT	6,634	1.68	2023, 2024
Netherlands NLD	6,563	1.71	2023, 2024
Switzerland CHE	6,108	1.76	2023, 2024
Belgium BEL	5,990	1.28	2023, 2024
Portugal PRT	5,983	1.07	2023, 2024
Iceland ISL	5,953	1.63	2023, 2024
Germany DEU	5,926	1.63	2023, 2024
Hong Kong SAR, China HKG	5,874	0.921	2024
Ireland IRL	5,753	1.59	2023, 2024

World Bank, World Development Indicators
Kaufmann, D. and A. Kraay, Worldwide Governance Indicators, World Bank

Sources

Researchers

Researchers in R&D (per million people)

UNESCO Institute for Statistics · CC BY 4.0 · updated quarterly

Researchers counted as full-time equivalents (two half-time researchers count as one), from national research surveys that many countries run only now and then. So coverage is thin outside the OECD.

Rule of law

Rule of Law (estimate)

World Bank · CC BY 4.0 · updated annual

How this was computed

Data used: most recent value in 2010-2025; values come from 2010–2024. To adjust for income, each measure is first predicted from GDP per person (in percentage terms, on a log scale) with a straight-line fit. Only what is left over is then compared. This is called a partial correlation. The line is drawn the standard way (ordinary least squares), which picks the line that comes closest to all the countries at once. The error margins allow for countries in the same region resembling each other, using 7 World Bank regions. The q-value corrects for testing all 12,497 pairs at once, using the Benjamini–Hochberg method. Underlying data last updated DYB 2024. How the country data works · explore Researchers and Rule of law

This page shows that two measures go together. It does not show that Researchers changes Rule of law, or the reverse. These figures also describe countries, not individual people. See the ecological fallacy.